If $27^8=9^q$, what is $q$?
Answer: We begin by expressing both sides of the equation in terms of the base 2: $(3^3)^8=(3^2)^q$, which simplifies to $3^{24}=3^{2q}$. Setting the exponents equal to each other, $24=2q$, or $q=\boxed{12}$.